when we use EIS to analyze the ionic conductivity of solid state electrolyte, we often find the calculated ionic conductivity of grain boundary is larger than that of grain, what's the reason? does it mean that a much higher total ionic conductivity can be obtained when the grain size become smaller and smaller?
Dear Jianguo Sun ,
Grain boundaries are defects that scatter carriers, thus reducing their mobility. Therefore smaller grains result in a higher density of defects and an increase in the resistivity. So, higher the resistivity suggests low conductivity contribution from grain & analogously higher conductivity contribution from grain boundaries. Now, interestingly this effect becomes pronounced once the grain size reaches the carrier's mean-free path (MFP) values; further reducing the grain size would result in a considerable resistivity increase. So, by reducing the grain size consistently, you may initially get an increase in ionic conductivity but after it reaches carrier's MFP values, it'll again decrease.
Regards,
KP
Dear Jianguo Sun,
When a bulk material is produced, the total binding energy of the bulk increases as the size is increased.
A single crystal has large binding energy than a bulk of the same material consisting of small grains.
It means the atoms and hence the associated electrons are more tightly bound and increases the resistance . This means decreases the conductivity.
This can be verified experimentally by EIS.
Thermodynamically, the larger the grain size, the entropy is less ( This can be thought of very easily by the idea of randomness ).
So, small grain size has the larger probability of electrons to exist out side the bulk potential of a grain.
As the grain is smaller, the no of grains inside a material of same size , increases. Means total contribution of probability of existence of electrons outside the grains increases which leads to higher conductivity.
One more important point to mention is the interaction between boundaries which is also responsible for increasing the conductivity.
It is better to realise the idea by the following simple model.
Suppose two potential wells separated by a large distance.
An electron in each well has a probability to exist outside the well.
When the two well are well separated , there is negligible interaction between them. As the wells are taken closer and closer, the interaction increases giving higher probability of electrons of each well to exist in the space between the wells. Means electrons become more and more free which leads to higher conductivity.
But once the two wells are forming a single coupled potential well ( means a single bulk formed by two smaller grains ) , the conductivity reduces. This is the quantum mechanical explanation as far I understand.
This can be theoretically calculated .
Thanks and Regards
N Das
In brief: ions have to overcome local potential barriers (provided by the other atoms around), when diffusing through a material. Because the potential barriers are often lower on average along the grain boundary (or on a free surface) in comparison to the ones in the bulk, according to the Arrhenius law, the grain boundary diffusivity (and with it ionic mobility and subsequently ionic conductivity) is often higher than that in the bulk. BR, René
This paper has proved the amorphous structure of the grain boundary in LATP, they also gave a simulation on the ion conductivity of grain and grain boundary. The simulated results show the ionic conductivity of grain boundary is lower than that of the grain, which is in line with my previous understanding. (see: Adv. Energy Mater. 2021, 2100707. DOI: 10.1002/aenm.202100707),
Then, let's turn our eyes to this question. I found it may be caused by the experiment setup, for example, when I once used the multiple-channels and single-channel Solartron electrochemical stations to test the EIS of the same pellet, respectively. The results are slightly different and the result tested from single-channel equipment is in line with my understanding that the ionic conductivity of the grain is larger than that of the grain boundary.
However, we cannot exclude the effect from the material itself. Such as doping during synthesis, which will precipitate at the grain boundary and may cause a positive effect on the ionic conductivity. Besides, the inhomogeneous distributation of Li in the grain could also be a reason for the lower ionic conductivity. In general, we need to combine different experimental evidence to dig the truth behind.
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